The present invention relates to a technology of compression/expansion in a two-dimensional signal, and more particularly to a technology of encoding and decoding the two-dimensional signal employing a wavelet transform.
When the two-dimensional signal that is typified by an image signal is stored in a record medium, or is transmitted via a network, data compression or data encoding is indispensable in order to efficiently utilize a record medium and a transmission path. Conventionally, various techniques such as predictive encoding and encoding employing DCT (Discrete Cosine Transform) have been proposed, and are being used actually. In recent years, the information compressing method employing a wavelet transform has been vigorously studied, and various proposals therefor have been made.
The wavelet transform is, as to speak, subband encoding, in which repeating a subband division of dividing the band in both of a horizontal direction and a vertical direction with respect to a low-frequency band side allows a multi-hierarchy band division to be carried out. Such a band division is called an octave division. When the band is divided as far as a third hierarchy, ten subbands as shown in FIG. 16 can be obtained. Herein, each of 3LL, 3LH, 3HL, and 3HH is a subband of a least significant hierarchy, each of 2LH, 2HL, and 2HH is a subband of a hierarchy higher than it, and each of 1LH, 1HL, and 1HH is a subband of a most significant hierarchy. Further, LH is a subband low-pass-filtered in a horizontal direction and high-pass-filtered in a vertical direction, HL is a subband high-pass-filtered in a horizontal direction and low-pass-filtered in a vertical direction, and HH is a subband high-pass-filtered in both of a horizontal direction and a vertical direction. Each subband includes a wavelet transform coefficient. The wavelet transform coefficient being included in each subband is called a subband coefficient in this Specification. Further, while the wavelet transform, in general, is carried out for each color component such as YCbCr (YUV), the wavelet transform coefficients of all color components that correspond to an identical hierarchy/identical position are called one subband coefficient in a lump in this specification. Further, each color component belonging to an identical subband coefficient is called a component of the subband coefficient.
The wavelet transform, which is characterized in being capable of hierarchically expressing one piece of an image by overlapping image components each having a plurality of resolutions, in having less peculiar distortion and noise that stems from a block structure, for example, a block distortion of a JPEG technique, or the like, is adopted for the technique such as JPEG2000. However, the wavelet transform is used in combination with an entropy coding method that enables each subband coefficient to be efficiently compressed because the wavelet transform itself has no compression effect.
For example, JPEG2000 employs arithmetic encoding as an entropy encoding technique, in which the subband coefficient is decomposed into bit planes, are divided into encoding blocks having a constant size in each subband, and then are subjected to the arithmetic encoding (for example, see Patent document 1).
Further, in Non-patent document 1, a set of coefficients corresponding to an identical space coordinate are extracted from an LH subband, an HL subband, and an HH subband belonging to an identical hierarchy to constitute a vector. Specifically, for example, three coefficients picked up from an identical space position of 3LH, 3HL, and 3HH one by one constitute a three-dimensional vector, and 12 coefficients picked up from 2×2 blocks of an identical space position of 2LH, 2HL, and 2HH four by four constitute a 12-dimensional vector. Next, the vector of which power (magnitude) is in the vicinity of zero is quantized to zero, and is classified as a invalid vector, and all coefficients belonging to the invalid vector are excluded from to-be-encoded coefficients. And, the valid vector is vector-quantized with a codebook corresponding to a class of power of the above vector.
On the other hand, a Huffman code is known as one of the entropy encoding techniques, and an image encoding device as well for encoding each subband coefficient by employing the Huffman code has been proposed (for example, see Patent document 2).    [Patent document 1] JP-P2003-274185A    [Patent document 2] JP-P2002-112039A    [Non-patent document 1] Shuitsu MATSUMURA, Michiaki KATO, Tsuyoshi TAKEBE “Wavelet Image Coding Using Power Adaptive Vector Quantization”, 1995 Image Coding Symposium (PCSJ95), October, 1995, pp 121-122